Vibratory gyroscopes with resonator attachments

ABSTRACT

Disclosed herein are vibratory gyroscopes comprising hollow shell resonators and methods of fabricating thereof. Specifically, a vibratory gyroscope comprises a support substrate comprising a substrate primary surface and a resonator support surface, substantially perpendicular to the substrate primary surface. The gyroscope also comprises a hollow shell resonator comprising a resonator inner surface and a resonator outer surface such that the resonator inner surface defines a recessed region with a recessed region opening facing the substrate primary surface. At least one of the inner or outer resonator surfaces is attached to the resonator support surface of the support substrate adjacent to the inner edge surface of the resonator. The inner edge surface can be formed by a hollow stem with or without opening through this surface. Furthermore, the resonator support surface can be a continuous cylindrical surface or a segmented surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. § 119(e) of USProvisional Patent Application 63/378,297, filed on 2022 Oct. 4, whichis incorporated herein by reference in its entirety for all purposes.

BACKGROUND

Vibratory gyroscopes, which may be also referred to as vibratingstructure gyroscopes, use vibrating structures (e.g., resonators) todetermine various parameters (e.g., rotation rates). Specifically, avibrating object continues to vibrate in the same direction even whenthis object (or the entire gyroscope) rotates. Vibratory gyroscopes canbe made smaller and cheaper than other types of gyroscopes whileproviding high accuracy. These features make vibratory gyroscopesparticularly useful in many devices such as smartphones and otherelectronic devices for use in a variety of applications such as consumerproducts, autonomous systems, space, and defense.

SUMMARY

Disclosed herein are vibratory gyroscopes comprising hollow shellresonators and methods of fabricating thereof. Specifically, a vibratorygyroscope comprises a support substrate with a substrate primary surfaceand a resonator support surface, substantially perpendicular to thesubstrate primary surface. The gyroscope also comprises a hollow shellresonator with a resonator inner surface and a resonator outer surfacesuch that the resonator inner surface defines a recessed region with theopening facing the substrate primary surface. The inner and/or outerresonator surface is attached to the resonator support surface of thesupport substrate adjacent to the inner edge surface of the resonator.The inner edge surface can be formed by a hollow stem with or without anopening through this surface. Furthermore, the resonator support surfacecan be continuous or segmented.

Clause 1. A vibratory gyroscope comprising: a primary axis; a supportsubstrate comprising a substrate primary surface and a resonator supportsurface, extending substantially perpendicular to the substrate primarysurface; and a hollow shell resonator comprising a resonator innersurface, a resonator outer surface, an inner edge surface, and an outeredge surface, wherein: the resonator outer surface is opposite of andseparated by a wall thickness from the resonator inner surface, theouter edge surface extends between the resonator inner surface and theresonator outer surface, having an annulus shape, and facing thesubstrate primary surface, the inner edge surface is surrounded by theresonator inner surface, positioned closer to the primary axis than theouter edge surface, and facing the substrate primary surface, theresonator inner surface defines a recessed region having a recessedregion opening extending between the outer edge surface and the inneredge surface, having an annulus shape, and facing the substrate primarysurface, the resonator outer surface extends to the inner edge surfaceor is separated from the inner edge surface by the wall thickness, andat least one of the resonator inner surface and the resonator outersurface is attached to the resonator support surface of the supportsubstrate adjacent to the inner edge surface.

Clause 2. The vibratory gyroscope of clause 1, wherein the resonatorouter surface extends to the inner edge surface and defines a resonatorpassthrough opening such that the inner edge surface has an annulusshape and surrounds the resonator passthrough opening.

Clause 3. The vibratory gyroscope of clause 1, wherein the resonatorouter surface is separated from the inner edge surface by the wallthickness defines a resonator blind opening such that the inner edgesurface has a circular shape defined by the resonator inner surface.

Clause 4. The vibratory gyroscope of clause 1, wherein the resonatorinner surface is attached to the resonator support surface of thesupport substrate.

Clause 5. The vibratory gyroscope of clause 4, wherein the resonatorsupport surface, to which the resonator inner surface is attached, isformed by an outer support protrusion, extending from the substrateprimary surface substantially parallel to the primary axis.

Clause 6. The vibratory gyroscope of clause 4, wherein the resonatorsupport surface, to which the resonator inner surface is attached, isformed by a substrate recess extending from the substrate primarysurface along the primary axis.

Clause 7. The vibratory gyroscope of clause 4, wherein the resonatorouter surface is further attached to the resonator support surface ofthe support substrate formed by an inner support protrusion, extendingfrom the substrate primary surface along the primary axis.

Clause 8. The vibratory gyroscope of clause 4, wherein the resonatorouter surface is not attached and spaced away from the resonator supportsurface of the support substrate.

Clause 9. The vibratory gyroscope of clause 4, wherein the resonatorouter surface is attached to the resonator support surface of thesupport substrate while the resonator inner surface is not attached andspaced away from the resonator support surface of the support substrate.

Clause 10. The vibratory gyroscope of clause 1, wherein the inner edgesurface is separated from the support substrate by a gap.

Clause 11. The vibratory gyroscope of clause 1, wherein the inner edgesurface is attached to the support substrate.

Clause 12. The vibratory gyroscope of clause 11, wherein the resonatorouter surface extends to the inner edge surface and defines a resonatorpassthrough opening such that the inner edge surface has an annulusshape and surrounds the resonator passthrough opening.

Clause 13. The vibratory gyroscope of clause 11, wherein the resonatorouter surface is separated from the inner edge surface by the wallthickness and defines a resonator blind opening such that the inner edgesurface has a circular shape defined by the resonator inner surface.

Clause 14. The vibratory gyroscope of clause 13, wherein the inner edgesurface is entirely attached to the support substrate.

Clause 15. The vibratory gyroscope of clause 13, wherein the inner edgesurface is partially attached to the support substrate such that aportion of the inner edge surface is exposed.

Clause 16. The vibratory gyroscope of clause 1, wherein the resonatorsupport surface is continuous, forming a cylindrical surface symmetricalabout the primary axis.

Clause 17. The vibratory gyroscope of clause 1, wherein the resonatorsupport surface is segmented and formed by a plurality of segmentsdistributed about the primary axis.

Clause 18. The vibratory gyroscope of clause 17, wherein each adjacentpair of the plurality of segments is separated by a support surface gap.

Clause 19. The vibratory gyroscope of clause 1, wherein the recessedregion of the hollow shell resonator has a half-toroidal shape.

Clause 20. The vibratory gyroscope of clause 1, further comprising aplurality of primary surface electrodes, wherein: the plurality ofprimary surface electrodes is positioned on and substantially parallelto the substrate primary surface, aligned and offset relative to theouter edge surface by a primary surface electrode gap, and the pluralityof primary surface electrodes is uniformly distributed about the primaryaxis.

Clause 21. The vibratory gyroscope of clause 20, wherein the pluralityof primary surface electrodes is formed by capacitive sensingelectrodes.

Clause 22. The vibratory gyroscope of clause 20, further comprising aplurality of side electrodes, wherein: the plurality of side electrodesextends substantially perpendicular to the substrate primary surface andis aligned and offset relative to the resonator outer surface by a sideelectrode gap, and the plurality of side electrodes is uniformlydistributed about the primary axis.

Clause 23. The vibratory gyroscope of clause 22, wherein the pluralityof side electrodes is formed by capacitive sensing electrodes.

Clause 24. The vibratory gyroscope of clause 1, wherein each of theresonator inner surface and the resonator outer surface is formed by ametal.

Clause 25. The vibratory gyroscope of clause 1, wherein: the hollowshell resonator has a height of less than 10 cm, and the hollow shellresonator has a diameter of less than 10 cm.

These and other embodiments are described further below with referenceto the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a bottom perspective view of a hollow shell resonator (for usein a vibratory gyroscope) illustrating the resonator's inner surface andstem, in accordance with some examples.

FIG. 2 is a perspective partial cross-sectional view of a vibratorygyroscope comprising a support substrate and a hollow shell resonator,supported on the substrate using the resonator's inner and outersurfaces, in accordance with some examples.

FIGS. 3A-3E are cross-sectional side views of a vibratory gyroscopeillustrating different types of support substrates and stem ends, inaccordance with some examples.

FIGS. 4A-4C are cross-sectional side views of different types ofattachments between the resonator's inner and outer surfaces and thesupport substrates, in accordance with some examples.

FIGS. 5A-5F are cross-sectional side views of different types ofattachments between the resonator surfaces and the support substrate, inaccordance with some examples.

FIG. 6A is a cross-sectional side view of a vibratory gyroscopecomprising a support substrate and a hollow shell resonator,illustrating the various openings in the support substrate, inaccordance with some examples.

FIG. 6B is a top view of the support substrate of the vibratorygyroscope shown in FIG. 6A, in accordance with some examples.

FIG. 7A is a cross-sectional side view of a vibratory gyroscopecomprising a support substrate and a hollow shell resonator,illustrating the various openings in the support substrate, inaccordance with some examples.

FIG. 7B is a top view of the support substrate of the vibratorygyroscope shown in FIG. 7A, in accordance with some examples.

DETAILED DESCRIPTION

In the following description, numerous specific details are outlined inorder to provide a thorough understanding of the presented concepts. Thepresented concepts may be practiced without some or all of thesespecific details. In other instances, well-known process operations havenot been described in detail to not unnecessarily obscure the describedconcepts. While some concepts will be described in conjunction with thespecific embodiments, it will be understood that these embodiments arenot intended to be limiting.

INTRODUCTION

Disclosed herein are vibratory gyroscopes, which may be also referred toas micro-vibratory gyroscopes. For example, a vibratory gyroscope mayhave a hollow shell resonator with a height of less than 10 cm and/or adiameter of less than 10 cm. Unlike other types of gyroscopes (e.g.,dynamically tuned gyroscopes, ring laser gyroscopes), vibratorygyroscopes use support substrates and resonators (e.g., hollow shellresonators, tuning-fork resonators, ring resonators) with specificresonator-to-substrate attachments. Specifically, vibratory gyroscopesdescribed herein have at least a portion of this resonator-to-substrateattachment or, more specifically, the attachment interface that extendsin a substantially perpendicular direction to the substrate's primarysurface. For purposes of this disclosure, the term “substantiallyperpendicular” is defined as an angle between 80° and 100° or, morespecifically, between 85° and 95° (or less than 10° deviation from thenormal or even less than 5° deviation). This attachment interface mayalso be referred to as a side attachment.

Without being restricted to any particular theory, it is believed thatsuch orientation of the attachment interface (i.e., the side attachment)helps to significantly improve the performance of the vibratorygyroscopes, in comparison to the attachment interface extendingsubstantially parallel to the substrate's primary surface (which may bereferred to as a bottom attachment). The side attachment is found to besuperior to the bottom attachment (i.e., inner edge surface attachment)because the side attachment produces lower maximum von Mises stress nearthe attachment interface normalized to the energy stored in theresonator (i.e., normalized von Mises stress). A finite element method(FEM) simulation found that a significant reduction (e.g., about 40%) inthe normalized von Mises stress can be achieved by switching from thebottom attachment to the side attachment. This stress reduction couldlead to lower anchor loss, higher Q, lower sensitivity of Q tothermo-residual and package stress at the attachment surfaces, and lowertransmission of acoustic energy between the support substrate and theresonator through the attachment surfaces and the hollow stem. Overall,the side attachment is more tolerant to shock and vibration events.

In one example, a fused-silica 3D shell resonator with an open-endedhollow stem, a radius of 2.5 mm, a height of 2.5 mm, a radius of 0.5 mmfor the attachment region, and a shell thickness of approximately 70micrometers at the outer edge surface and the inner edge surfacedeflecting in the n=2 wine-glass mode at a frequency of approximately 13kHz was used for FEM. The analysis found that when the hollow stem isattached to the support Zsubstrate only from the inner edge surface (thebottom-only attachment), the maximum von Mises stress at the inner edgesurface normalized to the mechanical energy stored in the resonator is39.408 MPa/J. When the resonator is attached from only the sidewallsurfaces (the sidewall only attachment) of the hollow stem which is theresonator inner surface (length=300 micrometers), the maximum von Misesstress in the hollow stem near the resonator support surface and the atthe inner edge surface normalized to the mechanical energy stored in theresonator is 23.832 MPa/J. When the resonator is attached from both thesidewall surface of the hollow stem (which is the resonator innersurface (length=300 micrometer)) and the entire inner edge surface, themaximum von Mises stress in the stem near the resonator support surfacenormalized to the mechanical energy stored in the resonator is 23.825MPa/J.

Furthermore, vibratory gyroscopes described herein have hollow shellresonators that form/comprise hollow stems/hollow anchors. This type ofhollow-shell resonator can be referred to as a hollow-stem resonator ora hollow-anchor resonator (or a hollow-shell hollow-stem resonator).Specifically, the stem has a cavity that extends substantially to theinner edge surface of the hollow shell resonator and, in some examples,can be open to the support substrate. Alternatively, the cavity can bedefined by a resonator blind opening. In other words, the cavity can beseparated from the support substrate by a thin wall defined by the inneredge surface and the resonator outer surface. This thin wall may haveabout the same (e.g., within 70% or even within 35% thickness) as theaverage wall thickness of the hollow shell resonator. This thin wall canbe referred to as a stem. However, this wall should be distinguishedfrom conventional bulky stems of conventional resonators, which do nothave cavities in the stem portion and which can be referred to assolid-stem resonators or solid-anchor resonators.

It has been found that hollow-stem resonators performed differently (andgenerally better) than solid-stem resonators due to the lowerthermoresidual stress near the support interface component of the hollowshell resonators. Specifically, when the resonator is attached to asupport substrate via an interface component material having differentcoefficients of thermal expansion (CTE), hollow shell resonators tend tobe more flexible and less bulky (thereby causing more deflection andless thermoresidual stress) than solid-anchor resonators. Finite elementmethod (FEM) simulations were performed on both types of resonators. Inthese simulations, the two types of resonators have the same distancebetween the center axis and the outer edge surface (a.k.a., the shellouter radius of 2.5 millimeters), the same distance between the centeraxis of the resonator and the edge of the inner edge surface (a.k.a.,the anchor post radius of 320 micrometers), and the same size of theouter edge surface (a.k.a., the rim thickness of 70 micrometers). Thesame resonator material (i.e., fused silica) and the same supportsubstrate material (i.e., silicon or borosilicate glass) were also used.Specifically, the von Mises stress of the shell resonators near thesupport interface component after the resonators are attached to thesupport substrates via the interface material at 325° C. and cooled downto room temperature (25°) was identified. It has been found that theamount of thermoresidual stress (i.e., von Mises stress caused by CTEdifference between the resonator, interface material, and supportsubstrate material after temperature change) for the solid-stemresonator is about 30% higher than for the hollow-stem resonator.

In some examples, a vibratory gyroscope comprises a hollow shellresonator, which may be also referred to as a micro-mechanicalresonator. For example, the resonator may have the shape of athree-dimensional (3D) hollow half-hemispherical shell (a half-toroid).The resonator may have a hollow cylindrical stem defining a primary axisof the vibratory gyroscope. The hollow feature of the shell resonator isdefined by the spacing between the resonator's inner and outer surfaces.This spacing may also be defined as a wall thickness. It should be notedthat the wall thickness may vary at different portions of the hollowshell resonator. In some examples, these variations are within 70% oreven within 35%.

The resonator's inner and outer surfaces also define an outer edgesurface, which extends between the resonator's inner and outer surfaces,has an annulus shape, and faces the substrate's primary surface. Aninner edge surface is surrounded by the resonator's inner surface and ispositioned closer to the primary axis than the outer edge surface. Theinner edge surface also faces the substrate's primary surface. Theresonator inner surface defines a recessed region having a recessedregion opening (e.g., a passthrough opening or a blind opening)extending between at least the inner edge surface, having an annulusshape, and facing the substrate primary surface. The resonator's outersurface extends to the inner edge surface (when the hollow stem has ordefines a resonator passthrough opening) or is separated from the inneredge surface by the wall thickness (when the stem has or defines aresonator blind opening).

The resonator is attached to a support substrate. The resonator isattached to the support substrate through at least one of the inner orouter surfaces of this hollow stem, which differentiates vibratorygyroscopes described herein from conventional gyroscopes. Planar,vertical, and three-dimensional curved capacitive electrodes are formedon the support substrate to sense the vibration motion of the resonatorand to force the resonator into resonant vibration. Other types ofmotion sensing methods, such as optical sensing, are also within thescope of some examples. The support substrate could be fabricated usingvarious micro-electromechanical systems (MEMS) fabrication processessuch as the silicon-on-glass (SOG) process and the silicon-on-insulator(SOI) process.

As noted above, the distinguishing feature of the vibratory gyroscopesdescribed herein or, more specifically, of the gyroscopes' devicestructure is the attachment of the resonator's central stem to thesupport substrate through at least a portion of the resonator stem innerand/or outer surfaces. These surfaces may extend substantially parallel(e.g., within 10° or even within 5°) to the gyroscope's primary axis.This type of attachment (in comparison with attachment only through theresonator stem inner edge surface that faces the support substrate andextends substantially perpendicular to the gyroscope's primary axis)improves the robustness of the resonator attachment (especially undershock, vibration, and temperature variations), reduces the effect ofsubstrate stress (induced by temperature variation or the package) onthe device, and reduces the amount of acoustic energy dissipated throughthe hollow stem and the attachment surfaces to the supporting substrate(a.k.a. anchor loss). This attachment through the inner or outersurfaces attachment could result in the increase of the overallmechanical quality factor (Q) by reducing the transfer of acousticenergy between the support substrate and the 3D shell resonator throughthe hollow stem and the attachment surfaces reducing the sensitivity ofQ to thermoresidual or package stress in the attachment surfaces region,and increasing of the maximum stress or the force before the resonatoris detached from the support substrate. This attachment also improvesthe shock/vibration resistance of the attachment (at the anchor regionwhere the resonator is attached to the support substrate) since theresonator is more solidly attached to the substrate and will not producehighly localized points of stress under shock, vibration, or largetemperature swings.

Examples of Vibratory Gyroscopes

FIG. 1 illustrates one example of a hollow shell resonator 120, whichhas a three-dimensional (3D) half-toroid hemispherical shell shape. Thehollow shell resonator 120 can be symmetrical around its primary axis101. The hollow shell resonator 120 comprises an outer edge surface 125(which may be also referred to as a rim), a stem 127, and a recessedregion 150, extending between the outer edge surface 125 and the stem127 and defined by the resonator outer surface 123. The stem 127 iseffective protrudes in the middle of the recessed region 150 and is usedfor attaching the hollow shell resonator 120 to a support substrate (notshown in FIG. 1 ). Specifically, the stem 127 is defined by theresonator inner surface 122 (as the stem's outer surface relative to theprimary axis 101) and by the resonator outer surface 123 (as the stem'sinner surface relative to the primary axis 101). The stem 127 terminateswith the inner edge surface 124, which can extend between the resonatorinner surface 122 and the resonator outer surface 123 when the stem 127has a resonator passthrough opening 128, e.g., as shown in FIG. 1 . Inthis example, the inner edge surface 124 has an annulus shape.Alternatively, the stem 127 may have a resonator blind opening 129, inwhich case, the inner edge surface 124 is surrounded by the resonatorinner surface 122 and has a circular shape (e.g., as shown in FIG. 3Cbelow). In this example, the bottom of the stem cavity is separated fromthe inner edge surface 124 by a wall thickness that may deviate lessthan 70% or even less than 35% from the average wall thickness of thehollow shell resonator 120. For purposes of this disclosure, the wallthickness is defined as the distance between the resonator outer surface123 and the resonator inner surface 122.

The hollow shell resonator 120 has an axisymmetric shape, meaning thatthe hollow shell resonator 120 is symmetric around its primary axis 101.The inner edge gap 121 can be parallel to the central longitudinal axisof the stem 127. The resonator inner surface 122 partiallyencloses/surrounds a recessed region 150, forming an annulus shapearound the stem 127. The recessed region 150 may be curved, e.g.,forming hemispherical, elliptical, or other shapes.

The stem 127, through which the hollow shell resonator 120 is attachedto the support substrate 110, has the shape of a hollow tube or acylinder with an opening 128 in the middle. Its primary axis 101 extendsthrough this opening 128. The opening 128 can be a through opening(e.g., as shown in FIGS. 1 and 2 ) or a bling opening (e.g., as shown inFIGS. 3C-3E)

In some examples, this “stem” cylinder does not have a uniform diameter(within planes parallel to the X-Y plane) along its entire length (alongthe Z axis). For example, the diameter may increase as the distance fromthe inner edge surface 124 increases. The length of the stem 127 can bedefined by the distance between the inner edge surface 124 and the mostdistant point (from the recessed region opening 152) on the resonatorinner surface 122 or the resonator outer surface 123. The length of thestem 127 may be also referred to as a height and can be comparable to,shorter than, or longer than the height of the overall hollow shellresonator 120, e.g., defined by the outer edge surface 125 and theturning point (the topmost point) of the resonator outer surface 123.The turning point (the topmost point) of the resonator outer surface 123is also the most distant point from the recessed region opening 152.

To operate as a vibratory gyroscope or, more specifically, as amechanical vibratory gyroscope, the hollow shell resonator 120 is forced(i.e., driven) to mechanically vibrate in the flexural mode. Thevibratory gyroscope 100 can be driven in the fundamental flexural modes(a.k.a. n=2 wine-glass modes) because of these modes' high gyroscopicscale factor. In the n=2 wine-glass mode, the hollow shell resonator 120vibrates such that the outer edge surface 125 (i.e., the shell rim)flexes from a circle to a first ellipse, and then back to a circle, andthen to a second ellipse whose long axis is rotated 90° from that of thefirst ellipse. In the other n=2 wine-glass mode, the flexural modevibration pattern is 45° rotated from the first flexural mode. Thisvibration pattern also shows the outer edge surface 125 (i.e., the shellrim) of the hollow shell resonator 120 going from a circle to anellipse, then back to a circle, and then to an ellipse whose long axisis rotated 90° from the first ellipse. In each mode, the ellipsesintersect at points where the outer edge surface 125 (i.e., the shellrim) does not move (called a node) and where the outer edge surface 125(i.e., the shell rim) flexes the maximum amount (anti-node). The nodesand antinodes of the two flexural modes are rotated 45° relative to eachother. The vibratory gyroscope 100 can also be operated by driving theresonator in higher flexural modes, such as n=3 wine-glass modes, n=4wine-glass modes, etc.

FIG. 2 is a schematic partial cross-sectional view of vibratorygyroscope 100, in accordance with some examples. This type of avibratory gyroscope can be also referred to as a 3D-shell resonatorgyroscope. Overall, a vibratory gyroscope comprises a mechanicalresonator (operable as a vibrating mass) and electrodes that excite andmeasure the vibrating motions of the mechanical resonator. Vibratorygyroscopes measure rotation rates (or angles) by detecting the amountsof the Coriolis Force. The Coriolis Force is proportional to therotation rate and vibrating velocity, effective mass, and angular gainof a mechanical resonator. The mechanical resonator has one or multiplemechanical resonance modes that can be excited by (i.e., mechanicallycoupled by) the Coriolis Force. Many existing vibratory gyroscopes, suchas microelectromechanical systems (MEMS) gyroscopes, have planarmechanical resonators made with a flat substrate. 3D shell resonatorgyroscopes can be more desirable than planar resonator gyroscopes due topotentially better structural symmetry, higher mechanical qualityfactor, and better shock and vibration insensitivity.

The vibratory gyroscope 100 (shown in FIG. 2 ) comprises a 3D shellresonator 120, and a support substrate 110. The vibratory gyroscope 100also comprises primary surface capacitive electrodes 170 and sidecapacitive electrodes 172, both of which can be formed from a conductivematerial and placed either underneath the outer edge surface 125 (i.e.,the primary surface electrodes 170) on the support substrate 110 and/oraround the resonator inner surface 122 (not shown) or the resonatorouter surface 123 near the outer edge surface 125 (i.e., the sidecapacitive electrodes 172). The outer edge surface 125 does not touchthe support substrate 110 or either of the primary surface capacitiveelectrodes 170 or the side capacitive electrodes 172. Instead, the outeredge surface 125 is separated (from the substrate and electrodes) fromthem by a gap (e.g., 0.1-200 micrometers or, more specifically, 10-100micrometers). This gap is sometimes referred to as an air gap eventhough the interior of the vibratory gyroscope 100 surrounding thehollow shell resonator 120 can be a vacuum environment.

In some examples, the hollow shell resonator 120 is attached (anchored)to the support substrate 110 or, more specifically, to the resonatorsupport surface 112 of the support substrate 110 using one or moresupport interface components 160. Some examples of such supportinterface components 160 include metal solder (e.g., gold/tin (Au/Sn)solder, gold/indium (Au/In) solder), sintering metal nanoparticles(e.g., gold (Au) nanoparticles, silver (Ag) nanoparticles, copper (Cu)nanoparticles), conductive epoxy, and glass frit.

As noted above, the stem 127 of the hollow shell resonator 120 ishollow. The inner edge surface 124 of stem 127 can be either open (i.e.,the stem opening 128 is a through opening) or closed (i.e., the stemopening 128 is a blind opening). When the inner edge surface 124 isclosed, the inner edge surface 124 has the shape of a flat circlelocated at the center of the hollow shell resonator 120, which issubstantially parallel to the substrate primary surface 111 and connectsthe non-parallel regions of the resonator inner surface 122. When theinner edge surface 124 is open, the inner edge surface 124 has the shapeof a ring parallel to the substrate primary surface 111 near the centerof the hollow shell resonator 120 and connects the resonator innersurface 122 and resonator outer surface 123. The shell stem 127 can beattached to the resonator support surface 112 either through a portionof the resonator outer surface 123, a portion of the resonator innersurface 122, the inner edge surface 124, or through any combination ofthese three surface portions, as will be described later. There aresignificant advantages to attaching the hollow shell resonator 120 tothe support substrate 110 through at least a portion of the resonatorinner surface 122 or a portion of the resonator outer surface 123 asdescribed above with reference to the side attachment (vs. the bottomattachment).

FIGS. 3A-3E show cross-sectional views of a few examples of thevibratory gyroscope 100 (e.g., a 3D shell resonator gyroscope) withdifferent attachments between the support substrate 110 and hollow shellresonator 120. Specifically, FIG. 3A shows an example of thecross-section of the vibratory gyroscope 100, in which the shell stem127 is a hollow stem with an open-end face (i.e., an open-ended hollowstem). The shell stem 127 is attached to the resonator support surface112 formed by a portion of the inner support protrusion 113 and theouter support protrusion 114. Specifically, the resonator inner surface122 faces and is attached to the outer support protrusion 114, while theresonator outer surface 123 faces and is attached to the inner supportprotrusion 113. The support interface components 160 can be used forthis attachment, e.g., one support interface component 160 positionedbetween and connecting the resonator inner surface 122 and the outersupport protrusion 114, another support interface component 160positioned between and connecting the resonator outer surface 123 andthe inner support protrusion 113. In this FIG. 3A example, the inneredge surface 124 is separated from the substrate primary surface 111 byan inner edge gap 121. The outer edge surface 125 is separated from thesubstrate primary surface 111 by the primary surface electrode gap 171.In some examples, the inner edge gap 121 is the same as the primarysurface electrode gap 171. Alternatively, the inner edge gap 121 isdifferent than the primary surface electrode gap 171. This stemattachment configuration is also shown in FIG. 2 and further describedbelow with reference to FIG. 4C. Some potential benefits of theseattachment examples (e.g., shown in FIG. 2 and FIG. 4C, over otherexamples) include better shock resistance because the stem 127 ismechanically supported from both resonator inner and outer surfaces.

FIG. 3B shows an example of the vibratory gyroscope 100 (e.g., a 3Dshell resonator gyroscope) with the open-ended stem 127 attached to thesupport substrate 110 only through at the resonator inner surface 122,i.e., a portion of the resonator inner surface 122 proximate to theinner edge surface 124. It should be noted that the resonator innersurface 122 can also be viewed as the outer surface of the stem 127. Inthis example, the resonator support surface 112 is in a recess 115 withthe support substrate 110, i.e., the recess 115 extending below thesubstrate primary surface 111. Specifically, the inner edge surface 124extends into the recess 115. Some potential benefits of this example (inFIG. 3B) are easier microfabrication processes (e.g., versus the examplein FIG. 3A), lower thermoresidual stress at the resonator supportsurface (e.g., versus the example in FIG. 3C). Specifically, the 3Dhollow shell resonator has a smaller mechanical stiffness near theresonator support surface, which helps to reduce the stress.

FIG. 3C shows an example of the vibratory gyroscope 100 (e.g., a 3Dshell resonator gyroscope) with the closed-ended stem 127 that isattached to the outer support protrusion 114. Specifically, theresonator inner surface 122 faces the outer support protrusion 114 andis attached to the outer support protrusion 114 using a supportinterface component 160. In this example, the outer support protrusion114 is positioned above the substrate primary surface 111 such that theinner edge surface 124 also protrudes above the substrate primarysurface 111. Some potential benefits of the attachment example in FIG.3C is a simpler microfabrication process (versus the one in FIG. 3A) andhas better shock resistance because of the larger mechanical stiffnessof the 3D hollow shell resonator near the resonator support surface(versus the one in FIG. 3B).

FIG. 3D shows the cross-section of another example of vibratorygyroscope 100 in which outer support protrusion 114 has an offset (alongthe X-axis) between the interface with support interface component 160and support substrate 110. In some examples, this offset (along theX-axis) is between 0.01-10 millimeters or, more specifically, between0.1-5 millimeters, depending on the size of a 3D shell resonator. Forexample, for a 3D shell resonator with a diameter of 5 millimeters, thevalue could be 10 micrometers to 4.5 millimeters). In this example,support substrate 110 is shown to be connected to outer case 119. Theconnecting distance between the interface of hollow shell resonator 120and support interface component 160 and outer case 119, which isprovided by a combination of outer support protrusion 114 and supportsubstrate 110 is identified as D1. In some examples, this connectingdistance (D1) is between 0.01-10 millimeters or, more specifically,between 0.1-5 millimeters, depending on the size of a 3D shellresonator. For example, a 3D shell resonator with a diameter of 5millimeters may have a connecting distance (D1) of millimeters or, morespecifically, 0.1-3 millimeters. It should be noted that this connectingdistance (D1) extends along both the X-axis and the Z-axis and dependson the thickness of the support substrate 110. As a reference, thethickness of support substrate 110 is between 0.01-10 millimeters or,more specifically, between 0.1-5 millimeters, depending on the size of a3D shell resonator. For example, for a 3D shell resonator with adiameter of 5 millimeters, this value could be 0.1-2 millimeters.

FIG. 3E shows the cross-section of yet another example of vibratorygyroscope 100 in which support interface component 160 is positionedbetween the inner edge surface 124 and support substrate 110. In thisexample, the connecting distance between the interface of the hollowshell resonator 120 and support interface component 160 and the outercase 119 (identified as D2) is a combination of the thickness ofinterface component 160 and the thickness of support substrate 110. Insome examples, this connecting distance (D2) is between 0.01-10millimeters or, more specifically, between 0.1-5 millimeters dependingon the size of a 3D shell resonator. For example, for a 3D shellresonator with a recessed region diameter of 5 millimeters, this valuecould be 0.1-2 millimeters.

FIGS. 4A-4C show examples of various resonator stem attachment schemeshighlighting the geometrical relationship between the shell stem 127,support interface component 160, resonator support surface 112, outersupport protrusion 114, and inner support protrusion 113. It should benoted that the inner support protrusion 113 and/or outer supportprotrusion 114 can be also replaced with the recess 115 (as describedabove with reference to FIG. 3B.

FIG. 4A shows the close-up view of an example where a portion of theresonator inner surface 122 of an open-ended stem 127 is attached to theresonator support surface 112 of the outer support protrusion 114 usingthe support interface component 160. The resonator stem 127 can also bea close-ended stem. The stem 127 can be also attached to the resonatorsupport surface 112 defined in a recess 115 formed in the supportsubstrate 110, instead of a support protrusion formed on or attached tothe support substrate 110.

FIG. 4B shows the close-up view of another example where a portion ofthe resonator outer surface 123 is attached to the resonator supportsurface 112 of the inner support protrusion 113 using the supportinterface component 160. The stem 127 can be also attached to theresonator support surface 112 defined in a recess 115 formed in thesupport substrate 110, instead of a support protrusion formed on orattached to the support substrate 110.

FIG. 4C shows the close-up view of another example where a portion ofthe resonator inner surface 122 and a portion of the resonator outersurface 123 are attached to the substrate's outer support protrusion 114and the substrate's inner support protrusion 113, respectively, usingthe support interface component 160. This example was described abovewith reference to FIG. 3A. The stem 127 can be also attached to theresonator support surface 112 defined in a recess 115 formed in thesupport substrate 110, instead of a support protrusion formed on thesupport substrate 110.

FIGS. 5A-5F show examples of the stem attachment schemes highlightingthe relationship between the geometrical relationship between the stem127, inner edge surface 124, support interface component 160, resonatorsupport surface 112, inner support protrusion 113, outer supportprotrusion 114, support substrate 110, and inner edge gap 121.Specifically, FIG. 5A shows the close-up view of another example where aportion of the resonator inner surface 122, which is the outer surfaceof the hollow stem 127, is attached to the resonator support surface 112of the outer support protrusion 114 using the support interfacecomponent 160. The inner edge surface 124 is separated from thesubstrate primary surface 111 by a controlled gap called the inner edgegap 121.

FIG. 5B shows the close-up view of another example where a portion ofthe resonator inner surface 122 of the open-ended hollow stem 127 isattached to the resonator support surface 112 of the outer supportprotrusion 114 (using the first component portion 161 of the supportinterface component 160) and at least a portion of the inner edgesurface 124 of the open-ended hollow stem 127 is attached to thesubstrate primary surface 111 (using the second component portion 162 ofthe support interface component 160). In other examples, the resonatorhollow stem 127 can also be a closed-ended hollow stem.

FIG. 5C shows the close-up view of another example where a portion ofthe resonator inner surface 122 and a portion of the resonator outersurface 123 of the open-ended hollow stem 127 are attached to theresonator support surfaces 122 on the outer support protrusion 114 andthe inner support protrusion 113, respectively, using the firstcomponent portion 161 of the support interface component 160 and thethird component 163 of the support interface component 160. Furthermore,at least a portion of the inner edge surface 124 of the hollow stem 127is attached to the substrate primary surface 111 using the secondcomponent portion 162 of the support interface component.

FIG. 5D shows the close-up view of another example where a portion ofthe resonator inner surface 122 of the closed-ended hollow stem 127 isattached to the resonator support surface 112 on the outer supportprotrusion 114 using the first component portion 161 of the supportinterface component 160. Furthermore, the entire surface of the inneredge surface 124 of the closed-ended hollow stem 127 is attached to thesubstrate primary surface 111 using the second component portion 162 ofthe support interface component 160.

FIG. 5E shows the close-up view of another example where a portion ofthe resonator inner surface 122 of the closed-ended hollow stem 127 isattached to the resonator support surface 112 on the outer supportprotrusion 114 using the first component portion 161 of the supportinterface component 160. Furthermore, a portion of the inner edgesurface 124 of the closed-ended hollow stem 127, which is away from itsprimary axis 101, is attached to the substrate primary surface 111 usingthe second component portion 162 of the support interface component 160.

Finally, FIG. 5F shows the close-up view of another example where aportion of the resonator inner surface 122 of the closed-ended hollowstem 127 is attached to the resonator support surface 112 on the outersupport protrusion 114 using the first component portion 161 of thesupport interface component 160. Furthermore, a portion of the inneredge surface 124, closest to/surrounding/including the primary axis 101of the closed-ended hollow stem 127 is attached to the substrate primarysurface 111 using the second component portion 162 of the supportinterface component 160.

Overall, attaching the hollow shell resonator 120 to the supportsubstrate 110 through at least a portion of the resonator inner surface122 and/or the resonator outer surface 123 is desirable due to loweranchor loss, higher mechanical Q, lower temperature sensitivity, loweracoustic energy transmission between the support substrate to theresonator through the hollow stem and the attachment surfaces, lowerthermal stress transmission from the support substrate to the resonatorthrough the attachment surfaces, and significantly improved mechanicalsupport during shock or vibration events that prevent high levels ofmechanical stress regions where the shell is attached to the substrate.Some of these benefits are described above.

The Q factor for a micromechanical resonator is affected by anchor loss,material quality, thermoelastic damping, phonon-phonon dissipation, airdamping, and surface loss. The Q of a micromechanical resonator made ofan amorphous material such as amorphous fused-silica or a single-crystalmaterial such as single-crystal silicon at a vibrating frequency (f)lower than 1 MHz at an ambient pressure less than a few milli Torr tendsto be dominated by anchor loss, surface loss, and thermoelastic damping.

When a 3D shell resonator is vibrating (moving) in the flexuralresonance mode, the hollow stem is also vibrating (moving, deflecting)in the flexural resonance mode although the vibration amplitude of thehollow stem is significantly smaller than that of the outer edge surface(i.e., the resonator rim). The deflection amplitudes of differentlocations within the hollow stem have a strong dependence on the radialdistance from the primary axis at the center of the device. Thedeflection amplitude is the largest at a location furthest from theprimary axis and vice versa. The deflection amplitudes of differentlocations within the hollow stem are a weak function in the directionparallel to the primary axis.

When the hollow stem of a 3D shell resonator is attached to the supportsubstrate only from the inner edge surface, non-uniform stress isdeveloped in the radial direction in the inner edge surface when theresonator is deflecting in a flexural mode. Large stress is developed atthe location furthest from the primary axis and almost no stress isdeveloped near the center of the device.

When the hollow stem is attached from the sidewall surfaces to thesupport substrate, the radial distances from the primary axis to alllocations within the resonator support surfaces are nearly the same, anduniform stress is developed at all locations of the resonator supportsurface. When a resonator deflects in the flexural mode, the maximumstress developed in the hollow stem close to the resonator supportsurface is smaller than the maximum stress when the hollow stem isattached only from the inner edge surface to the support substrate.

When the hollow stem is attached to the support substrate from both thesidewall surface and the inner edge surface to the support substrate,the maximum stress developed in the hollow stem near the resonatorsupport surface is smaller than when the hollow stem is attached to thesupport substrate only from the inner edge surface. This is becauseimproved mechanical support is provided from the resonator supportsurface on the sidewall of the hollow stem.

In all of the configurations shown in these figures, the shell isattached to the substrate in the attachment regions throughout theentire perimeter of the hollow stem. In other words, the attachmentsurface surrounds the entire stem and extends up the stem by somedistance. FIGS. 6A-6B and 7A-7B show two more different configurationswhereby the hollow shell resonator 120 can be attached to the supportsubstrate 110 by modifying the design of the resonator support surface112.

FIGS. 6A-6B show a modified arrangement for the vibratory gyroscope 100support attachment surfaces. Specifically, FIG. 6A illustrates a sidecross-sectional view of a vibratory gyroscope 100 comprising a supportsubstrate 110 and hollow shell resonator 120 such that the supportsubstrate 110 has two portions, i.e., a first substrate portion 602 anda second substrate portion 604. The first substrate portion 602 is usedfor attaching the hollow shell resonator 120 or, more specifically, tothe sidewall surface of the hollow stem (which could be closed-ended oropen-ended). The second substrate portion 604 is attached to the firstsubstrate portion 602 and provides support to the electrodes.

FIG. 6B illustrates a top view of the first substrate portion 602showing various openings in the first substrate portion 602.Specifically, the first substrate portion 602 comprises a first opening610 where the stem of the hollow shell resonator 120 protrudes. Thefirst opening 610 provides the resonator support surface for attachingthe stem. The first substrate portion 602 also comprises a second set ofopening 620, selectively removed between a part supporting the stem andthe part positioned on the other sides of the second set of opening 620.The second set of opening 620 provides stress isolation between theseparts or, more generally, between the support substrate 110 and thehollow shell resonator 120 thereby reducing the amount of energy lossfrom the hollow shell resonator 120 to the support substrate 110, thusincreasing the Q. Similar structural designs (to the one shown in FIG.6A-6B) can be made for the inner support protrusion or a recess of thesupport substrate.

FIGS. 7A-7B illustrate another example of the vibratory gyroscope 100.Specifically, FIG. 7A illustrates a side cross-sectional view of avibratory gyroscope 100 comprising a support substrate 110 and hollowshell resonator 120 such that the support substrate 110 has twoportions, i.e., a first substrate portion 602 and a second substrateportion 604. The first substrate portion 602 is used for attaching thehollow shell resonator 120 or, more specifically, to the sidewallsurface of the hollow stem (which could be closed-ended or open-ended).The second substrate portion 604 is attached to the first substrateportion 602 and provides support to the electrodes. Referring to FIG.7B, unlike the example in FIG. 6B, the part of the first substrateportion 602 between the first opening 610 and the second set of opening620 is now segmented and may be referred to as segmented portions 615.In other words, the first opening 610 and the second set of opening 620are interconnected by additional openings 617 that segment this part ofthe first substrate portion 602. These segmented portions 615 are usedto support the hollow shell resonator 120 around the perimeter of thehollow stem (in this case the attachments are shown on the insidesidewall of the resonator facing the recessed region, although theattachment could also be on the outside or both inside and outsidesidewalls) only in selected segments. The segments are attached to theportion of the protrusion that is attached to the substrate's primarysurface, using extended beams, or springs. This configuration furtherprovides mechanical isolation between the shell resonator and thesupport substrate reduces anchor loss and increases Q, and also reducesthe effects of stress induced in the substrate on the performance of theshell. FIG. 7B shows the top view of the segmented portions of theattachment region to more clearly illustrate their geometry.

The 3D shell micro resonator gyroscope with an attachment scheme from atleast a sidewall portion of the hollow stem can be fabricated in anumber of different ways by using MEMS fabrication processes, includingbut not limited to the silicon-on-glass (SOG) process or thesilicon-on-insulator (SOI) process.

CONCLUSION

Although the foregoing concepts have been described in some detail forpurposes of clarity of understanding, it will be apparent that certainchanges and modifications may be practiced within the scope of theappended claims. It should be noted that there are many alternative waysof implementing processes, systems, and apparatuses. Accordingly, thepresent embodiments are to be considered illustrative and notrestrictive.

The invention claimed is:
 1. A vibratory gyroscope comprising: a primaryaxis; a support substrate comprising a substrate primary surface and aresonator support surface, extending substantially perpendicular to thesubstrate primary surface; and a hollow shell resonator comprising aresonator inner surface, a resonator outer surface, an inner edgesurface, and an outer edge surface, wherein: the resonator outer surfaceis opposite of and separated by a wall thickness from the resonatorinner surface, the outer edge surface extends between the resonatorinner surface and the resonator outer surface, having an annulus shape,and facing the substrate primary surface, the inner edge surface issurrounded by the resonator inner surface, positioned closer to theprimary axis than the outer edge surface, and facing the substrateprimary surface, the resonator inner surface defines a recessed regionhaving a recessed region opening extending between the outer edgesurface and the inner edge surface, having an annulus shape, and facingthe substrate primary surface, the resonator outer surface extends tothe inner edge surface or is separated from the inner edge surface bythe wall thickness, and at least one of the resonator inner surface andthe resonator outer surface is attached to the resonator support surfaceof the support substrate adjacent to the inner edge surface.
 2. Thevibratory gyroscope of claim 1, wherein the resonator outer surfaceextends to the inner edge surface and defines a resonator passthroughopening such that the inner edge surface has an annulus shape andsurrounds the resonator passthrough opening.
 3. The vibratory gyroscopeof claim 1, wherein the resonator outer surface is separated from theinner edge surface by the wall thickness and defines a resonator blindopening such that the inner edge surface has a circular shape defined bythe resonator inner surface.
 4. The vibratory gyroscope of claim 1,wherein the resonator inner surface is attached to the resonator supportsurface of the support substrate.
 5. The vibratory gyroscope of claim 4,wherein the resonator support surface, to which the resonator innersurface is attached, is formed by an outer support protrusion, extendingfrom the substrate primary surface substantially parallel to the primaryaxis.
 6. The vibratory gyroscope of claim 4, wherein the resonatorsupport surface, to which the resonator inner surface is attached, isformed by a substrate recess extending from the substrate primarysurface along the primary axis.
 7. The vibratory gyroscope of claim 4,wherein the resonator outer surface is further attached to the resonatorsupport surface of the support substrate formed by an inner supportprotrusion, extending from the substrate primary surface along theprimary axis.
 8. The vibratory gyroscope of claim 4, wherein theresonator outer surface is not attached and spaced away from theresonator support surface of the support substrate.
 9. The vibratorygyroscope of claim 4, wherein the resonator outer surface is attached tothe resonator support surface of the support substrate while theresonator inner surface is not attached and spaced away from theresonator support surface of the support substrate.
 10. The vibratorygyroscope of claim 1, wherein the inner edge surface is separated fromthe support substrate by a gap.
 11. The vibratory gyroscope of claim 1,wherein the inner edge surface is attached to the support substrate. 12.The vibratory gyroscope of claim 11, wherein the resonator outer surfaceextends to the inner edge surface and defines a resonator passthroughopening such that the inner edge surface has an annulus shape andsurrounds the resonator passthrough opening.
 13. The vibratory gyroscopeof claim 11, wherein the resonator outer surface is separated from theinner edge surface by the wall thickness and defines a resonator blindopening such that the inner edge surface has a circular shape defined bythe resonator inner surface.
 14. The vibratory gyroscope of claim 13,wherein the inner edge surface is entirely attached to the supportsubstrate.
 15. The vibratory gyroscope of claim 13, wherein the inneredge surface is partially attached to the support substrate such that aportion of the inner edge surface is exposed.
 16. The vibratorygyroscope of claim 1, wherein the resonator support surface iscontinuous, forming a cylindrical surface symmetrical about the primaryaxis.
 17. The vibratory gyroscope of claim 1, wherein the resonatorsupport surface is segmented and formed by a plurality of segmentsdistributed about the primary axis.
 18. The vibratory gyroscope of claim1, wherein the recessed region of the hollow shell resonator has ahalf-toroidal shape.
 19. The vibratory gyroscope of claim 1, furthercomprising a plurality of primary surface electrodes, wherein: theplurality of primary surface electrodes is positioned on andsubstantially parallel to the substrate primary surface, aligned andoffset relative to the outer edge surface by a primary surface electrodegap, and the plurality of primary surface electrodes is uniformlydistributed about the primary axis.
 20. The vibratory gyroscope of claim19, further comprising a plurality of side electrodes, wherein: theplurality of side electrodes extends substantially perpendicular to thesubstrate primary surface and is aligned and offset relative to theresonator outer surface by a side electrode gap, and the plurality ofside electrodes is uniformly distributed about the primary axis.